The evolution of materials at an atomistic level may have vital consequences for the properties of materials. Therefore, modelling long time scale behaviour of defects in a material is very important, particularly for those used in nuclear power plants. The materials used in nuclear power plants should have good mechanical properties to overcome the corrosive environment and high temperature. Examples of these materials are the austenitic stainless steel and the Ni-based alloys due to their high temperature properties. Molecular Dynamics (MD) and on the fly Kinetic Monte Carlo (otf-KMC) techniques have been used to model the radiation damage in austenitic stainless steel and the Ni-based alloys. This thesis represents the main findings obtained. Three potentials were implemented and used to study radiation damage in austenitic stainless steel. Structural properties such as the elastic constants for the point defects in the pure metals were first calculated. This was followed by calculating the formation energies and migration energies of vacancy and self interstitial defects in the pure metals. Different calculations were performed using each potential on the ternary alloy (Fe with 10 at.% Ni and 20 at.% Cr) and the binary alloy (Ni with 20 at.% Cr) . For example, the segregation in these alloys was investigated using Monte Carlo simulations and results obtained for both alloys at high temperature MD. Furthermore, the vacancy formation energies were calculated for both alloys using all the potentials. Radiation damage at Grain Boundaries (GBs) in fcc Ni and a Ni-Cr binary alloy has been studied using MD and otf-KMC techniques. From the results obtained, the mobility of interstitials were found to be higher than that of vacancies and tend to move quickly to the GB. Vacancies are found to migrate to the GB if they are near otherwise they tend to form clusters in the bulk. During the simulations, interesting mechanisms were observed for the point defects migration and recombinations. Large roughening at the GB was observed, especially in the alloy system and overall the total number of defects accumulated on the GB after multiple collision cascades were relatively small. The radiation in fcc Ni resulting from low energy collision cascades was also modelled using MD and otf-KMC techniques. This part of work aimed replicating the observations seen in experiment and trying to understand them. Recombinations between vacancies and interstitials were found to happen from large distances with low barriers. Most defects produced from low energy collision cascades were found to recombine or interstitials were found to form clusters. Modelling the evolution of the vacancies shows the possibility of producing Stacking Fault Tetrahedra (SFT) which were found to dissociate at 200°C.